Where does the surname Chaim come from?

There are many variations of this name from Chaim to Higham, Heyem. Hyams, Hyman and so on. As an alternative there is a Jewish Word 'Khayim' meaning 'life'. However Chaim or the variations is English in origin from Bedfordshire, Derbyshire and Essex shariing the same meaning of 'high homestead' recorded in about 1086